Question

Water flows at the rate of 10 m per min from a cylindrical pipe of radius 2.5 mm. A conical vessel of diameter 40 cm and depth 24 cm is filled with water flowing from this pipe. The time taken to fill the conical vessel is:

• A. < 30 mins
• B. 30 < t < 50 mins
• C. 50 < t < 75 mins
• D. >75 mins

Answer 1

The correct option is C 50 < t < 75 mins

Area = $\pi$r${}^2$ = 6.25 $\pi$

Rate of flow = ($\pi$r${}^2$x1000) mm${}^3$/min = 6250$\pi$ mm${}^3$/min

Volume of cone =$\frac{1}{3}$ $\pi$r${}^2$h = $\frac{1}{3}$ $\pi$ (200)${}^2$x 240 mm${}^3$ = 80$\pi$x40000 = 3200000$\pi$ mm${}^3$
Thus, total time taken is:
$\frac{\left(Volumeofconeinm{m}^3\right)}{\left(Rateofwaterflowin{mm}^3/min\right)}$ = 51.2min
Thus answer option (c) is correct.